Question: Given $ m \angle RPS = 4x + 47$, $ m \angle QPR = 2x + 7$, and $ m \angle QPS = 96$, find $m\angle QPR$. $P$ $Q$ $S$ $R$
Answer: From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Substitute in the expressions that were given for each measure: $ {2x + 7} + {4x + 47} = {96}$ Combine like terms: $ 6x + 54 = 96$ Subtract $54$ from both sides: $ 6x = 42$ Divide both sides by $6$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $m\angle QPR$ $ m\angle QPR = 2({7}) + 7$ Simplify: $ {m\angle QPR = 14 + 7}$ So ${m\angle QPR = 21}$.